"ive found I have to work very hard on a bike to get and hold a heart rate near race hm pace for even 5 minutes."
Generally your maximum HR on a bike will be lower than what you can reach running (typically ~10pbm lower). So you won't be able to maintain your running tempo HR on a bike - you need a new set of zones based on your bike max HR, or better still use power rather than HR as cougie mentioned
I think the thing to remember is sport (like life) is inherently unfair. There is no such thing as a level playing field, and whatever decision on whatever aspect will benefit some at the expense of others.